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Wear-out models for composite materials fatigue, and the "strange case" of Kassapoglou's "too good to be true" model

Mike Ciavarella's picture

Wear-out models have been very successful for fitting probabilistic SN
curves of composite materials.  The "strength-life equal rank
assumption"
wear-out models for fatigue of composite materials were
first presented by Hahn and Kim [1], and later as a fitting approach to fatigue
data by Sendeckyj [2].

This basically says that if we take a set of nominally identical specimen, made of same material, same manufacturing, same heat treatments, etc., and if a specimen is stronger than another in static
tests, it should also last longer.  It cannot be proved of course, because either you make a test of the specimen to static rupture, or you break it by fatigue. But it
makes sense. Also, it makes sense, statistically, that the ranking is such that the probability distribution should not cross, and should follow some order. Notice it is also not only very likely, but it greatly simplify things, and any other alternative hypothesis, I would be lost to guess what it could be.   We shall return to this later, when finding out that the second of Kassapoglou's model violates this assumption, but in an hidden form, not based on some evidence, but in an effort to produce some apparently ultra-simple results which he had obtained already before in the first model.   That these results are NOT in agreement with experimental evidence, it was found out in 3 independent large experimental validations later, unless he was so unlucky as to find as comparative terms by lack exactly the few cases where the match with experiments could be there.   However, anyone with basic knowledge of fatigue, before publishing any such result, should be extremely cautious, because it is obvious that the entire community will either promote you as the main contributor to fatigue of the last 2 centuries, or else risk to laugh at you!

 

 

Sendeckjy is today the standard procedure to fit SN data of composite
materials, especially in view of obtaining reliable estimates of scatter in
fatigue lives, which is used in the present expensive certification programs in
the building block approach, which results in the full scale testing being
accelerated with a LEF (Life Enhancement Factor) increase of the load, so as to
reduce the otherwise impossibly long fatigue testing necessary to ensure the
same reliability in primary composites structures, as was obtained with
metallic structures, as prescribed by the EASA-FAA certification agencies.

A significantly different and apparently "revolutionary"
 model has been proposed more recently by Kassapoglou [3,4,5] which is so
ambitious as to predict SN curves without any fatigue tests, but from static
tests alone!    

In his basic form, a wear-out process such that the probability of failure
cycle-by-cycle is constant, resulting in a SN curve which is obtained directly
from the distribution of static strength, without any fitting constant.
Curiously, making such assumption corresponds to saying that either you test
one specimen one cycle, than take another and make another cycle, or you
continue testing always the same specimen, as we all do in fatigue, it should
not matter!!

The reality is another.  Within these assumption, a specimen either
breaks at first cycle, or continues to live forever.  Kassapoglou's SN
curve has nothing to do with fatigue.  It is only the number of
"extractions" you have to make to fail a specimen, which obviously
increases for low stress.

No surprise that 3 independent groups have found Kassapoglou's predictions
very poor, resulting unconservative by various orders of magnitude in a FAA
2011 report [5], in a book regarding the mean stress effect [7], and also by
[14].  Surprising instead that his papers has tests which confirm his
theory. 

Considering these preliminary assumptions, it is not to take as
"proof" that some limited features of the predicted SN curve seem to
be in agreement with experimental data. Actually, by changing a little the
original derivation, computing the probability of "at least one failure" in the
life of a specimen, instead of "one and just one failure", permits to obtain
the SN curve in closed form for any quantile, for a 2-par Weibull static
strength distribution, showing the distribution of lives is a Weibull with
shape parameter 1, for any starting Weibull distribution of static strength.
This is close to the value of 1.25 found as typical in composites of
aeronautical interest in the thousands of data in the Navy database, which is
the important basis for the design and certification of present civil
aircrafts. 

Therefore, it is common belief that typical wear-out models relying on
actual SN data and having available fitting constants (Sendecky [2],
 Caprino-D'Amore [11-13]) tend to be more accurate than the original
Kassapoglou's method, if anything as they model reality, so should not properly
be considered "competitor" of this miracolous model.

 

A second model by Kassapoglou (2011) inserts wear-out, and situation
becomes even more confused!  The wearout is such that the same SN curve of
the unphysical model is reobtained!   Fantastic!    I have a
feeling that this very special wearout model simply violates the
"strength-life equal rank assumption", from which the "SN curve
uniquely dependent on static strength" is obtained as a special case.

 

By the way, we all would like to have a model of fatigue like that, it is
since 1860 that we are searching for it, and we haven't succeded.  On the
contrary, fatigue testing is a huge industry with hundreds of billions of
dollars spent, time allocated, thousands of researchers working on it in all
the world in the last 150 years.    Good reviews on fatigue explain
why static strength alone doesn't explain much.  So why Kassapoglou takes
so many risks of his reputation in this hugely ambitious claims?

 

 

References

[1] Hahn HT. Kim RY. Proof testing of composite materials. J Composite
Materials, 1975. vol 9, 297311.

[2] Sendeckyj G.P. Fitting Models to Composite Materials Fatigue Data. Test
Methods and Design Allowables for Fibrous Composites, ASTM STP 734, Chamis,
C.C. editor, ASTM, Philadelphia, 1981. 245-260

[3] C Kassapoglou, 2012. Predicting the Structural Performance of Composite
Structures Under Cyclic Loading, PhD thesis, Delft Univ of Technology.

http://repository.tudelft.nl/assets/uuid:73a4025dc519-4e3a-b1cdc1c8aa0fdfeb/full_document_v3.pdf

[4] C Kassapoglou, Fatigue Model for Composites Based on the Cycle-by-cycle
Probability of Failure: Implications and Applications, Journal of Composite
Materials February 1, 2011 45: 261-277.

[5] J Tomblin and W Seneviratne, 2011. DOT/FAA/AR-10/6: Determining the
Fatigue Life of Composite Aircraft Structures Using Life and Load-Enhancement
Factors,
www.tc.faa.gov/its/worldpac/techrpt/ar10-6.pdf

[6] R.S. Whitehead, H.P. Kan, R Cordero, and E.S. Saether, DOT/FAA/CT-86/39
(Navy Report Number NADC-87042-60) "Certification Testing Methodology for
Composite Structures," Volumes I and II, Report No. NADC-87042-60, October
1986. http://www.dtic.mil/dtic/tr/fulltext/u2/b112288.pdf

[7] AP. Vassilopoulos, T Keller, 2011. Fatigue of Fiber-reinforced
Composites, Springer-Verlag London

[8] ASTM E739 -- 91 Standard Practice for Statistical Analysis of Linear or
Linearized Stress-Life (S--N) and Strain-Life (e-N) Fatigue Data (2004)

[9]. J.M. Whitney, Fatigue characterization of composite materials. in
Fatigue of Fibrous Composite Materials, ASTM STP 723, American Society for
Testing and Materials (1981), pp. 133--151

[10] J.M. Whitney, I.M. Daniel, R.B. Pipes, Experimental Mechanics of Fiber
Reinforced Composite Materials (Prentice-Hall, Englewood Cliffs, 1984)

[11] A D'Amore, G Caprino, P Stupak, J Zhou, L Nicolais (1996) Effect of
stress ratio on the flexural fatigue behaviour of continuous strand mat
reinforced plastics. Science and Engineering of Composite Materials 5(1):1-8.

[12] G Caprino, A D'Amore. Flexural fatigue behaviour of random continuous
fibre reinforced thermoplastic composites. (1998) Composite Science and
Technology Volume 58,Issue 6, Pages 957-965

[13] A D'Amore, G Caprino, L. Nicolais, Marino G. (1999) Long-term
behaviour of PEI and PEI-based composites subjected to physical aging,
Composites Science and Technology, Volume 59, Issue 13, 1993-200

[14] J. Andersons, Yu. Paramonov, (2011) Applicability of empirical models
for evaluation of stress ratio effect on the durability of fiber-reinforced
creep rupture-susceptible composites, J Mater Sci (2011) 46:1705-1713 DOI
10.1007/s10853-010-4988-0

Comments

"This basically says that if a specimen is stronger than another in static tests, it should also last longer.  It cannot be proved of course. But it makes sense."

This statement can easily be proven false for a number of materials. Just pick two to compare-2024 and 7075 aluminum alloys. 7075 has higher static strength than 2024, yet 2024 fatigue life will exceed 7075 fatigue life, in both unnotched and notched coupons. If you are comparing one alloy (say aluminum) to another (say steel), then obviously both the static strength and the fatigue strength of steel will exceed that of aluminum for most steel alloys.

 

the link for the Kassapoglou thesis doesn't seem to work. I found it here though

http://repository.tudelft.nl/view/ir/uuid%3A73a4025d-c519-4e3a-b1cd-c1c8aa0fdfeb/

 

I don't do much composites testing, so I have little intuition or experience with them. Especially since composites are NOT homogeneous, AND their inhomogeneity has a substantial influence on the mechanical response in various tests, I would have guessed there was almost no way to derive a physics based model that related static strength to fatigue strength.

Mike Ciavarella's picture

dear Prost

thanks for your comment. It makes me think that I should explain. The equal rank assumption speaks amd refers to a set of nominally identical specimen of same material. Since there is scatter of static strength, Kassapoglou makes erroneously scatter of static strength to bemresponsible formfatigue SN curve.

 

For metals, one meeds a wear out model, and statisticsl one. Maybe I will write if anyone is interested.

 

mike 

Mike Ciavarella's picture

Dear Prost

 you probably have in mind the typical discussion on "fatigue ratio". This says the ratio between fatigue limit and static strength for a given class of materials.  Usually, crude approximations can be made on fatigue ratio based on hardness tests, for metals.

You find for any given class in any textbook about fatigue that fatigue ratio is nearly constant for a large range, meaning fatigue limit increases linearly with static strength, until a plateau is reached, when fatigue limit stays constant, no matter how much you increase static strength (with very high strength but generally brittle materials).

But all this shows that even if we relax the initial idea of equal rank assumption (which applies to a set of identical specimen), to class of materials, still it works!!  It is very hard to find a material that is stronger in fatigue and weaker in static strength.

Fleck and Ashby (1994), in an authoritative review which contains also data on composite materials, produce a large set of maps covering a huge number of references, and in particular show in Figure 5 the well-known fact that the endurance limit σ_{e} scales in a roughly linear way with the yield strength, σ_{y}.  Notice they choose yield strength instead of static ultimate strength for other reasons, and in this case, hidden there are other effects of ratio between yield and ultimate strength, but anyway, they are discussed in details if you want to have a look.

 

The fatigue ratio, defined as σ_{e}/σ_{y} (but more classically for metals, σ_{e}/σ_{fs}) at load ratio R =-1, appears as a set of diagonal contours. "The value of fatigue ratio, for engineering materials, usually lies between 0.3 and 1. Generally speaking, it is near 1 for monolithic ceramics, about 0.5 for metals and elastomers, and about 0.3 for polymers, foams and wood; the values for composites vary more widely--from 0.1 to 0.5". Naturally, for fatigue limit in composites (as well as ligth alloys), it is often intended the value at a given fixed number of cycles. This wide variation already makes one wonder that for composites the fatigue properties depend less on static properties than for other materials. A first alarm bells rings, with respect to Kassapoglou's claim. Moreover, Fleck and Ashby (1994) remark "The wide range of fatigue ratios shown by composites relates, in part, to the wide spectrum of materials used to make them, and to the necessarily broad definition of failure: in particulate composites, failure means fracture; in fibrous composites it means major loss of stiffness". 

NA Fleck, KJ Kang, MF Ashby - Acta metallurgica et materialia, 1994.  Overview no. 112: the cyclic properties of engineering materials 

http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/54.pdf

 

Mike Ciavarella's picture

I have added some files to the main post.

1) fitting models.... this is about Caprino-d'Amore and Sendeckyi (one is popular in Italy, the other in US, but they are similar and actually deserve comparisons), and why they produce more flexible results than the "too good to be true" K model.

2) Fleck 1994, the "standard" overview of fatigue

3) some example of fatigue ratio plots from al alloys and steel, for prost

4)  Sendecckyi original paper, which is hard to find

5) some Caprino papers also difficult

I confirm Prost' observation that fatigue in composites should be more complex than in metals, read: Fleck and Ashby (1994) remark "The wide range of fatigue ratios shown by composites relates, in part, to the wide spectrum of materials used to make them, and to the necessarily broad definition of failure: in particulate composites, failure means fracture; in fibrous composites it means major loss of stiffness". 

Also, this larger variation of fatigue ratio also suggests that static properties say LESS of fatigue properties than in metals, as Prost suggests.  So Kassapoglou's model is very naive indeed.

Mike Ciavarella's picture

Nobody should worry that his plane he is flying today may have been "certified" by Agencies (FAA, EASA), with Kassapoglou's method, only testing static properties!

You should be calm and trust the agencies, which would not trust a "theory" (not even if it were solid mathematically, as it is not, or confirmed by some experiments, and again it is not), without any testing.

It is true however, that industries tend to reduce fatigue testing the most.  And certification agencies tend to agree and negociate this with them, based on theories, sometimes solid, sometimes less so.

Three ways are known to reduce cost and time of testing,

  • accelerate testing, by incresing the load level (Life Enhancemenet Factor) which is based on some statistical MEASUREMENT of the scatter of fatigue livesand certainly not the Kassapoglou prediction of the scatter of fatigue lives
  • to omit low levels of stressing in testing in spectrum:  this could indeed work based on some theory, like Miner's rule for metals.  I suspect Kassapoglou is behind the so called Sikorsky method for omission levels (published also in previous edition of MIL 17 standards, and there is a reference in Kassapoglous phd thesis).  In fact, Kassapoglou was working almost 30 years in industry before writing his phd thesis.
  • to clip high loads

Further, agencies are now slowly accepting some reduction of testing based on evidence and building on previous experience.

 

I asked these 2 questions  to a man in certification agencies who has certified virtually every plane today in air with composite materials:

 

- Do we need fatigue tests (yet) to certify a composite structure?

- In case we need, how do we decide about the omission level for the spectrum?

 

I am asking him permission to publish his reply.   But the conclusion is that "Sikorsky method" to decide about the omission level was probably never used (except by Sikorsky itself?).  Given it relies on this fatigue theory which is very suspicious, should we warn Sikorsky at least?   Does anyone has contacts there? It depends also on how high they decided to truncate the spectrum.

In general it is arbitrarily but conservatively taken to be around 30% of limit loads. From an academic point of view, it could be higher, I know people who have argued that it could be 50 %DLL. But if you omit all loads below 50% DLL, it will remains so few loads in the spectrum that, at the end, it will not look like a fatigue test any longer.   And agencies don't buy this.  For the good of the safety of people!

 

So now, anyone can investigate if Sikorsky used more than 30% based on this very suspicious theory?

Mike Ciavarella's picture

Prost made some interesting discussion about metals.

Metals also wearout, although this is more in the form of a single crack forming, in initiation and propagation.  Paris law is a form of wearout law, although for initiation it is not known a good one.

Composites wearout in a simpler way in a sense, since you can easily see reduction of stiffnes and of residual strength.  Hence, the models of wearout. Residual strength is the "equivalent" of "crack size" if you like, when assessing damage tolerance.  So you design structures to have some damage (BVID) from the beginning, then test fatigue, and you still want some redisual strength at the end!

Anyway, from the point of view of statistical models, we should start step by step

  • if you assume deterministic static strength, and no wear out, there is nothing like fatigue
  • if you assume deterministic wear out and deterministic static strength, then you can immediately compute the SN curve, which will be a deterministic equation (this has some hopes to function in metals, since they are known not to have too much scatter in static strength, but they have scatter in fatigue lives, although not as high as composites). Hence, one would need to add some randomness in the wearout equation, see later). Notice that in this case the SN slope depends only on wearout constants.
  • if you now assume random static strength, and no wear out, then specimen shoud either fail at 1 cycle, or never fail. Notice this is the case of Kassapoglou first model, where he finds a SN curve!!   That SN curve is nothing close to fatigue, it is just the expected number of trials you have to make to pick a specimen having strength low enough to match your applied load!
  • assume random static strength, and deterministic wearout.  This is what Kassapoglou claims to do with his 2011 paper and in his 2012 thesis, but unfortunately, the wearout fitting constants misteriously disappear during the process (it is too long to explain what is wrong), and also the model returns exactly to the 2007 SN curve prediction.  Now this suggests that equal strength assumption is violated, but the model puts a little more realism to the 2007 result, although it becomes extremely rigid in the prediction. SN slope to depend only on scatter of static strength. The correct models should find slope from wearout constants (as in the simplest model above), and perhaps also a contribution from scatter of static strength, but marginal, depending on wearout model). The scatter of fatigue lives should NOT be constant, as in Kassapoglou, but depend again on the wearout constants. In these respect, we could say that Kassapoglou's model has chosen a wearout model which firstly violates equal strength assumption (maybe not largely), but more importantly, has imposed the wearout constants to be such that SN slope depends on scatter of static strength. In other words, Kassapoglou has imposed that wearout process is intrinsic in the static strength data. This is recursive reasoning. And obviously the result comes. But it is not necessarily true.   The experimental evidence of course shows that only some parts of the models are vaguely correct (like scatter of fatigue lives), whereas others (SN curve slope and mean value) are not corresponding to reality,
Mike Ciavarella's picture

Prost, for metals, one simple starting point could be deterministic static (as we know the variation is marginal at static strength), but random wearout, because we know we have scatter there.

This could be in the form of a random Paris law.  I guess in this case, some approach have been attempted, but they all are lacking some ingredients, since initiation is difficult to model, so they start with a large crack.  But sometimes, these authors are more experts of statistics than fatigue, and do not really improve things. 

But here are 3 possible important examples, including one is a book.

 

Random fatigue crack growth in mixed mode by stochastic collocation method

H Riahi, P Bressolette, A Chateauneuf - Engineering Fracture Mechanics, 2010 - Elsevier

... In the stochastic model proposed by Min and Qing-Xiong [27], the material parameters of
Paris-Erdogan crack growth law are considered as random variables and the distribution of the
FCG rate for a given crack length is obtained by Monte-Carlo ... Recently, Castillo et al. ...

Citato da 9 Articoli correlati Tutte e 4 le versioni Cita

A new probabilistic model for crack propagation under fatigue loads and its connection with Wöhler fields

E Castillo, A Fernández-Canteli, C Castillo… - … Journal of Fatigue, 2010 - Elsevier

... as in structural elements used in engineering practice, and consider a random crack growth ...
Extreme value theory (see Castillo [37]) and some compatibility conditions are used to derive ...
Most crack growth formulas have represented different versions of the Paris law (see Paris ...

Citato da 5 Articoli correlati Tutte e 5 le versioni Cita

[LIBRO] A unified statistical methodology for modeling fatigue damage

E Del Castillo, A Fernández-Canteli - 2009 - books.google.com

... 182 7.1.4 Random loading . . . . ... 31 E. Castillo, A. Fern´andez-Canteli, A Unified Statistical
Methodology for Modeling Fatigue Damage, c Springer Science + Business Media BV 2009 3
Page 16. ... 3. What sets of dimensionless variables can be used. For example, Paris et al. ...

Citato da 24 Articoli correlati Tutte e 9 le versioni Cita

 

Giuseppe Carbone's picture

Prof. Ing. Giuseppe Carbone - PhD
Associate Professor of Applied Mechanics
Politecnico di Bari

Giuseppe Carbone's picture

there are two serious mistakes in Kassapoglou's
model:

  1) 
the
first is related to the wear-out model, that he employs to predict the fatigue
life probability distribution. Given the fatigue stress sigma, his wear-out
model simply states that: i) all sample which have a static strength larger
than sigma will fail at the same given number of cycles n=N, ii) samples with
static strength less that sigma will all fail at cycle n=0. The wear out model
is, then, completely unphysical, since it states that, even under zero fatigue
load, all sample will fail at a given finite value n=N. The model can be corrected
by letting N depend on the static strength. But then we end up with a
qualitative different wear out model where the residual strength must depend on
n, sigma and static strength alone (N must not be explicitly included in the
model). Notwithstanding the weakness of the K's wear out model, one can even
wonder if it is possible to calculate the cumulate life probability
distribution of sample. In doing so one concludes that, since for n<N only
those samples with static strength less than fatigue load sigma may fail and
actually fail at cycle 0, the probability that a failure occurs in the first N
cycles is just given by the probability that the static strength is less than
the fatigue load sigma. Therefore the cumulate life distribution is constant
for the first n<N cycles and then jumps to 1 as the n>=N. Here is the
point where K made the second mistake

 
2) 
the
second K's mistake was indeed to consider that the constant life cumulate
distribution (for n<N) needed to be re-interpreted as a probability of
failure cycle per cycle (in other terms as a life probability density function if
one considers n as a continuous variable). But this is wrong, since what is constant
is the cumulate probability distribution and therefore the probability of
failure cycle per cycle is zero for 0<n<N. Indeed, as mentioned at point
1, samples may fail only at n=0 or n=N no failure can occur (because of the considered
wear-out model) in between. So the additional calculations presented by K are
simply wrong.

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Mike Ciavarella's picture

I tended to reason more physically, but you seem to point to more "rigorous" statements. I think your conclusions are connected to my "suspicion" that K fails to respect the "equal rank assumption", and probably a little more.

I suspect we can be able to write a correct model if we join forces.

Notice that Kassapoglou's model may well be a step backwards with respect to the existing Caprino-D'Amore and Sendeckyj's method, but at least, in his effort to produce a "prediction" of fatigue, he has raised a lot of interest, and I respect him. 

I hope he takes sportively the challenge we offer him to beat us now :)  !   And I am sure other people will get an interest, I received a few messages already...   It is possible that a better model, not as utopistic as Kassa's, but not as pure fitting as Caprino-D'Amore and Sendeckyj's method, can be found.

More to the point, when we have solid understanding, we can expand this to more complex cases.

Mike Ciavarella's picture

I have added in the main post a pdf for this paper which may be useful for the SLERA....

 

The Strength-Life Equal Rank Assumption and its application to the fatigue life prediction of composite materials

  • a Cranfield Institute of Technology and is now with the New Products Division of Ruston Gas Turbines Ltd, Lincoln, UK
  • b Analysis & Design Consultants Ltd, Newport Pagnell, UK
  • c Materials & Structures Department of the Royal Aircraft Establishment, Farnborough, UK

International Journal of Fatigue

Volume 10, Issue 3, July 1988, Pages 171–177

Abstract

The
authors have re-examined the Strength-Life Equal Rank Assumption
(SLERA) that is used in the fatigue life prediction of composite
materials, and suggest that this assumption may be valid for a wide
range of fibre-reinforced epoxy laminates subjected to tensile,
compressive or shear fatigue loadings. The evidence presented here
suggests that there may be an exact correlation between the initial
static strength and fatigue life expectancy. A corollary is that scatter
in the fatigue data is a consequence of the variation in the static
strengths of individual specimens. Using SLERA, an efficient and usable
life predictive technique has been developed for fibre-reinforced
composite materials.

 

Mike Ciavarella's picture

From the previous paper, I think there are important points.

Obviously SLERA is not use to show the unrealistic Kassapoglou's claim that static strength predicts everything, but:

 

  •  The paper will provide conclusive evidence for the validity
    of the SLERA. The argument that notched specimens invalidate
    the SLERA is false, because SLERA makes no assumption
    about residual properties. The SLERA states that there
    is a correlation between the static strength and the fatigue
    life expectancy of a sample of nominally identical components.
    As the fatigue life progresses, the strength of each
    component changes. For each component at a given cyclic
    life there is still a correlation between residual strength and
    residual life expectancy, but the correlation need not be the
    same as the initial one.

    • The scatter in fatigue data has two components, a fatigue

    component and a static one: The fatigue component is
    induced by variations in the propagation rates associated
    with the fatigue failure mechanisms. The static component
    is due to the variation in static strengths of the sample
    members under test, and may be visualized by taking a
    hypothetical SIN curve, Fig. 2. Take a set of specimens
    with static strengths that range from 500 to 1000 MPa, with
    a mean of 750 MPa, that are fatigue tested at 600 MPa.
    Specimens that have a strength less than 600 MPa will fail
    on loading, .that is they are effectively tested at 100% of
    their strength. Progressively stronger specimens are-effectively
    tested at lower percentages of their ultimate strength,
    thus specimens with a strength of 1000 MPa are tested at
    60% of their strength, and consequendy have longer fatigue
    life expectancies than weaker specimens. The SLERA will
    only apply if the fatigue component of the fatigue scatter
    is negligible, or else is some function of the static component.

    • The SLERA states that the stronger the specimen, the

    longer the life expectancy. As a result an exact correlation
    exists between strength and life expectancy. In addition the
    SLERA~ implies that the life expectancy is a function of
    the appli-~d load, therefore the lower the applied stress-the
    longer the fatigue life. This effectively defines the SIgN
    (stress-life) curve, therefore the SLER_A and the SIN curve
    are essentially the same.

    • It would appear that for fibre-reinforced epoxy

    laminates, the scatter in the fatigue data may be a direct
    consequence of variations in the static strength, ie there is
    no fatigue component. If there were a fatigue component,
    the experimental fatigue scatter bands should be greater than
    those for the static component alone. These findings strongly
    support the validity of the SLERA for the materials under
    investigation.

    • The main limitation of the SLERA is that it cannot predict

    a change in fatigue failure mode as a function of the stress
    level. Dhar,an9 suggested that for 'E'-glass/epoxy under
    tensile loadiag the dominant failure mechanism is a function
    of applied strain. Bamard et all° found that such a change
    in failure mechanism may lead to a discontinuity in the SIN
    curve, see Fig. 12. The SLERA appears to be valid above
    and below this discontinuity though the correlation between
    strerigth and life is different, s Unless a change in failure
    mode increases the slope of the SIN curve the SLERA will
    provide conservative estimates, see Fig. 13.

    • The SLERA cannot predict the residual strength,

    though some researchers have attempted to do so, eg Chou
    and Croman. 2

    THIS PART I AM NOT SURE, MAYBE GIUSEPPE CARBONE CAN INSTEAD OBTAIN IT !!!

    Conclusions
    1) The SLERA appears to be valid for a wide range of
    fibre-reinforced plastic laminates, provided there is no
    change in failure mode with fatigue life.
    2) The SLERA is a definition of the SIN curve, therefore
    the correlation between the strength and life is the SIN
    Curve.
    3) Scatter in fatigue data is primarily due to static strength
    variations, though additional scatter may occur in the
    region of a failure mode change.
    4) The scatter is a function of the applied stress, thus
    the lower the stress the lower the scatter; and is an
    inverse function of the slope of the S/N curve, thus
    the greater the slope the lower the scatter.
    5) A technique for predicting the static, fatigue and residual
    strength distributions from a small sample size
    has been suggested. This small sample size may allow
    testing of components without the prior requirement
    of laboratory specimen and scale model testing. This
    technique: can be easily computerized so that from input
    data comprising one static result and perhaps two sets
    of eight: fatigue results, the output data would be the
    static digtribution parameters, P-S-N curves

    S-N (probability of residual strength-stress-life)
    curves.

Mike Ciavarella's picture

 

Remember I posed two questions

 

- Do we need fatigue tests (yet) to certify a composite structure?

- In case we need, how do we decide about the omission level for the
spectrum?

 

Here is an answer from the man who was in the certification programs of all Airbus composite structures from the early A320, to A380, and the new A350.  Some people will recognize him, I have his permission to produce his text, but not his name.

 

 

Regarding metal structures, fatigue tests are systematically carried out
and they comprise two subsequent phases. The first one is a ‘crack free life’
demonstration, also so-called durability phase, starting with a brand new
structure and the second one is a ‘damage tolerance phase’ where artificial
cracks (sawcuts) are deliberately introduced in the test article to check crack
propagation assumptions. At Airbus, the minimum duration of each of these
sequences is at least 1.25 life (Design Service Goal).

A similar test protocol is used for composite structures with the same two
sequences. Regarding the first one, unlike metals, we start with a structure
representative of the minimum quality, with tolerable manufacturing flaws and
impact damages that will never be detected (up to BVID). In the second phase, we
do not introduce sawcuts but more severe accidental damages, detectable at
scheduled inspection intervals only, but not obvious. That means that we can fly
a whole inspection interval with such a damage. The purpose of this second phase
is to demonstrate the no-growth concept for these severe damage over one or two
inspection intervals (in case we miss the damage at the first inspection). The
purpose of the first phase was to demonstrate that no fatigue damage can
initiate from any discontinuity as initial flaws, impacts or stress
raisers.

Due to the very good feedback we have from service experience the first
sequence of the test protocol is more and more deleted and only the damage
tolerance demonstration phase remains. I can tell you that as far as the A380
program is concerned, the whole empennage (fin + horizontal stabilizer) has been
certified with only the second phase of the fatigue test protocol being carried
out. Although it is more and more accepted to forget the first phase of the test
protocol, deleting the second one is not foreseen in the near future.

As a conclusion, to certify a composite structure, Airworthiness
Authorities are still requiring at least a damage tolerance demonstration
focussing on the no-growth demonstration of severe accidental damages.

As far as a fatigue test, even with the Dam/Tol phase only, is
systematically foreseen, there is a need for developing a fatigue spectrum and
deciding about both truncation levels, clipping of high loads and omitting loads
below a certain level. In my past experience working with the Airworthiness
Authorities, I do not remember we have used the Sikorsky method to decide about
the omission level. In general it is arbitrarily around 30% of limit loads. From
an academia point of view, it could be higher, I know people who have argued
that it could be 50 %DLL. But if you omit all loads below 50% DLL, it will
remains so few loads in the spectrum that, at the end, it will not look like a
fatigue test any longer.

 

Dear Mike, this is very interesting indeed. Do you know if any predictive mechanistic fatigue models (e.g. of fatigue damage development or delamination growth) are used in design,if not certification phase of composite parts for aircraft?

Mike Ciavarella's picture

Dear Janis

 

 I am surprised you change topic.   Since your work on assessing Kassapoglou, is one of the 3 very independent which very sharply found it to be the worse around.  

 

Journal of Materials Science

March 2011, Volume 46, Issue 6, pp 1705-1713

Applicability of
empirical models for evaluation of stress ratio effect on the durability
of fiber-reinforced creep rupture–susceptible composites

Abstract

Fiber-reinforced
polymer–matrix composites are known to exhibit loading rate- and
time-dependent mechanical response. Their fatigue strength is determined
by a complex interaction of damage processes governed by loading
duration and cycle number. Apart from mechanistic approaches, a number
of empirical models of various sophistication have been proposed to
predict the durability of composites, differing in the amount of
experimental data needed for their application. The accuracy of several
such models is evaluated by comparing the prediction to the
experimentally determined stress ratio effect on fatigue life of glass
fiber-reinforced polyester–matrix composite. It is found that the
accuracy of prediction generally improves with increasing the amount of
test data needed for model calibration. However, the most accurate
method of fatigue life estimation, among the selected ones, is by the
modified Goodman diagram.


Journal of Materials Science
Journal of Materials Science

Look

Inside

 

I have added it to the list.

 

A recently proposed model [18, 19] is unique in the field
of composite fatigue studies in that it uses just static
strength characteristics (average and standard deviation) to
predict fatigue life at constant-amplitude cyclic loading.

 

 
So Kassapoglous model is [18, 19] in your paper.

 

The most economical, in terms of testing program necessary
for calibration, fatigue model relates the fatigue life
under cyclic loading to the distribution of static strength
[18, 19]. Treating subsequent load cycles as independent
strength tests with the probability of failure in a single test
given by p, the fatigue life N (defined as the number of
load cycles maximizing the function P, where P =
np(1 - p)n-1 is the probability of one and only one failure
between 1 and n cycles) is obtained as
N ¼
1
lnð1 pÞ
: ð1Þ
For the loading case of interest here, 0\R\1, the
cumulative failure probability is further approximated by
the two-parameter Weibull distribution

 

 

Based on tension tests [15], rst = 672 MPa and
s = 21 MPa. However, the fatigue diagrams predicted
according to Eq. 5 using these strength characteristics disagree
markedly with the fatigue test results (e.g., fatigue
strength for R = 0.1 is overpredicted by a factor of 1.5–1.9
within the experimental durability range). It should be noted
that the results are rather sensitive to the value of s [18

 

 


  As an alternative, s was treated as a fitting parameter and
its value determined so that Eq. 5 matched the fatigue test
data at R = 0.1. The value of s = 78 MPa (together with the
previous, experimental estimate of rst) provided a good
approximation of the fatigue data as seen in Fig. 1a. The
same best-fit estimate of s was further applied to predict the
S–N diagrams at the other stress ratios considered. It is seen
in Fig. 1b–e that the theoretical diagrams given by Eq. 5
systematically deviate from the experimental fatigue curves.
Specifically, Eq. 5 overestimates fatigue strength and
underestimates its reduction with the number of loading
cycles.

 

 

conclusion. The kassapoglou power law for SN curve works (and this is no surprise, it was found by Basquin in 1911 that they would), but the coefficient is wrong by a factor from 21 to 78 in stress, which is huge!     If you translate this to prediction of fatigue life, this becomes easily various orders of magnitude wrong!

 

So thanks Janis, for very important contribution.

 

Maybe I will study your work from Latvia much more.  It is unfortunate that your work is not well known in US, I think you deserve a lot more attention.  I hope Imechanica will help on that.

 

Mike Ciavarella's picture

I think Chapter
12 of CMH-17, Vol. 3 contains the most respected (and available in open
literature) treatments on the damage tolerance of composite materials
including damage resistance, damage growth, damage tolerance concepts
and durability concepts and analyses methods utilized in aircraft
design.  To my knowledge the damage resistance and damage growth
analyses are not accepted by regulatory authorities as the sole source
of validation.  Damage growth prediction is only in its infancy and
different classes of carbon fibers and composite materials (3-D weaving,
stitching, etc.) are being introduced continually.  One of the latest
being carbon nanostructures (CNS) or carbon nanostructures that are an
integral part of the fiber structure.  There is a lot of academic research of course, but the real industrial practice, and certification of real aircrafts, to my knowledge is this.  Hope this helps.

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella

Mike Ciavarella's picture

I have assigned to two undergraduates to study Caprino's method, and I mean Esther Accardi and Andrea Cito, but also all the others, please listen. I tried to summarize in 2 pages differences between models of Caprino love-and Kassa and Sendeckyj here:

http://imechanica.org/files/fitting_models_vs_kassapoglou.pdf

Of course these are preliminary thoughts. Sendeckyj and CDs have at the end very similar SN curves, and wearout models are not too dissimilar. Both CD and Sendeckjy get from "deterministic"  residual strength equation, as a particular case, the "deterministic" SN curve and they isolate the statit strength member to the RHS.  Since this is a statistical variable, and considering the SLERA, we obtain the distribution of lives, at different levels of applied voltage (ie. the probabilistic SN curves). The difference is, however, in addition to details on the form of the equations, also on the procedure for the fit. Sendeckky says to turn all the data from the deterministic equations (SN, residual, and runout censored) data as "equivalent static" and then does not fit a linere. CD (which have also included law for average voltage) instead make believe fit SN directly from the data (to determine the slopes and then all the constants of the wearout) and get the distributions of the screw, ie the SN probabilistic. In other words, CD is more "rudimentary" of Sendeckyj, which allows the use of all data (not only SN, but also residual and also static) for the best fit. Anyway the 2 models have never been compared with the experiments. We hope to do it ourselves, I have asked Caprino for the data. Meanwhile, we do better theoretical comparison that I have just mentioned.

In all this, Kassapoglou has some vague points which can be compared.  His wearout model is a special case, not really working in terms of SLERA, and the prediction do not need any fit of SN data.  As we say here, it is in another class, not "fitting" models, but "religious" models.  You must beleive in it :)

 regards

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella

Mike Ciavarella's picture

I think from the discussion so far, the conclusion is :-

 

   In the original K's model there is a confusion between what we call fatigue and statistics of the static strength of a number of specimens. Fatigue life (number of cycles) is mistakenly replaced with the number of tested specimens to find a specimen with strength less than applied load. This number of specimen is indeed solely depends on the initial statistical distribution of the static strength, while fatigue is related to damage accumulation in a specimen and its strength degradation with cycles, which contradicts the main assumption. One can also mistakenly deduce from the proposed model that if there is no dispersion in the static strength, for instance all the specimen have exactly the same statical strength, there is no such thing as an S-N curve.
    The probabilistic approach should come into consideration in a different way. If the sample did not break during the first cycle, then its probability of having strength greater than the applied load can be evaluated by the truncated distribution function. Then this random number will somehow decrease with the cycles and depending on the value of its static strength it will lead to a random value for its lifespan.
    K model is an interesting attempt of using wear-out models with degradation deterministic equations to predicting SN curves from static data only for components (something which is not easy even with metals). However, its result don't look realistic at all, and indeed we have explained here why. Not surprisingly, SN curves found in many independent assessments were found to be (generally) unconservative for the vast majority of data (10 sets) considered in FAA 2011 report [5], at least by 1-2 orders of magnitude.

Mike Ciavarella's picture

Kassapoglou's papers were accepted in the best or one of the best of the Composite materials journals.  How come the reviewers were so ineffective to improve the papers, given they claim such enormous result, and are so simple and the results look so perfect?   I miss something here.

Mike Ciavarella's picture

Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. Z. Gurdal

Samenstelling promotiecommissie:
Rector Magnicus


Prof. dr. Z. Gurdal


Prof. dr. ir. R. Benedictus 

TU Delft: Prof.dr.ir. Rinze Benedictus

Prof. dr. P.A. Lagace


Prof. dr. K.L. Reifsnider

Dr. Kenneth Reifsnider - Mechanical Engineering - University of ...

 

Prof. dr. ir. M.J.L. van Tooren


Prof. dr. M.R. Wisnom

Technische Universiteit Delft, promotor
Technische Universiteit Delft
Massachussetts Institute of Technology
The University of South Carolina
Technische Universiteit Delft
University of Bristol
Keywords: fatigue analysis, composite materials, damage, probability of
failure, residual strength
ISBN XXX-XX-XXXX-XXX-X
Copyright
c 2012 by Christos Kassapoglou

 

 

Except perhaps the supervisor of Kassapoglous's thesis (promoter), who doesn't look to me to have any experience of published record in fatigue at all, all the others are well known and respected scientists in fatigue of composite materials academic circles.  I am puzzled.  Maybe it is me after all to be completely wrong?

 

Yet, the 3 independent group of data are completely out of scale from Kassapoglou's theory.  It cannot be coincidence.  Theory is, I think, very weak if not completely wrong.   The claim is so huge, like if someone comes to you with a solution for cancer, by drinking water every other day.   And yet, all these respected people, they did not blink an eye.

 

 

Zafer Gurdal seems to be quite top class.  He is in fact faculty of at least 3 top universities.  Recently moved to South Carolina

 

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    Zafer Gürdal's
    Home Page. Professor. Departments of Aerospace and Ocean Engineering,.
    and Engineering Science and Mechanics. Blacksburg, VA 24061- ...

  3. [PDF]
    Zafer Gürdal Aerospace Structures Chair Faculty of Aerospace ...

    https://www2.aus.edu/conferences/iccst7/documents/prof_zafer_bio.pdf

    Zafer Gürdal.
    Aerospace Structures Chair. Faculty of Aerospace Engineering. Delft
    University of Technology (TU Delft). Prof. Gürdal received his B.S. in ...

 

Mike Ciavarella's picture

 

 

1

 

Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates Original Research Article
Composites Part B: Engineering, Volume 43, Issue 2, March 2012, Pages 354-360
Julien M.J.F. van Campen, Christos Kassapoglou, Zafer Gürdal

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Optimization of a composite cylinder under bending by tailoring stiffness properties in circumferential direction Original Research Article
Composites Part B: Engineering, Volume 41, Issue 2, March 2010, Pages 157-165
Adriana W. Blom, Patrick B. Stickler, Zafer Gürdal

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3

 

Design of variable-stiffness composite panels for maximum buckling load Original Research Article
Composite Structures, Volume 87, Issue 1, January 2009, Pages 109-117
Shahriar Setoodeh, Mostafa M. Abdalla, Samuel T. IJsselmuiden, Zafer Gürdal

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4

 

Design of variable–stiffness laminates using lamination parameters Original Research Article
Composites Part B: Engineering, Volume 37, Issues 4–5, June–July 2006, Pages 301-309
Shahriar Setoodeh, Mostafa M. Abdalla, Zafer Gürdal

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5

 

Design of variable-stiffness conical shells for maximum fundamental eigenfrequency Original Research Article
Computers & Structures, Volume 86, Issue 9, May 2008, Pages 870-878
Adriana W. Blom, Shahriar Setoodeh, Jan M.A.M. Hol, Zafer Gürdal

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6

 

Genetic algorithm optimization and blending of composite laminates by locally reducing laminate thickness Original Research Article
Advances in Engineering Software, Volume 35, Issue 1, January 2004, Pages 35-43
David B. Adams, Layne T. Watson, Zafer Gürdal, Christine M. Anderson-Cook

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7

 

Fiber path definitions for elastically tailored conical shells Original Research Article
Composites Part B: Engineering, Volume 40, Issue 1, January 2009, Pages 77-84
Adriana W. Blom, Brian F. Tatting, Jan M.A.M. Hol, Zafer Gürdal

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8

 

Optimization of course locations in fiber-placed panels for general fiber angle distributions Original Research Article
Composites Science and Technology, Volume 70, Issue 4, April 2010, Pages 564-570
Adriana W. Blom, Mostafa M. Abdalla, Zafer Gürdal

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9

 

Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters Original Research Article
Composite Structures, Volume 81, Issue 2, November 2007, Pages 283-291
Mostafa M. Abdalla, Shahriar Setoodeh, Zafer Gürdal

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10

 

Multi-step blended stacking sequence design of panel assemblies with buckling constraints Original Research Article
Composites Part B: Engineering, Volume 40, Issue 4, June 2009, Pages 329-336
Samuel T. IJsselmuiden, Mostafa M. Abdalla, Omprakash Seresta, Zafer Gürdal

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11

 

A genetic algorithm with memory for optimal design of laminated sandwich composite panels Original Research Article
Composite Structures, Volume 58, Issue 4, December 2002, Pages 513-520
Vladimir B Gantovnik, Zafer Gürdal, Layne T Watson

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12

 

Stacking sequence blending of multiple composite laminates using genetic algorithms Original Research Article
Composite Structures, Volume 56, Issue 1, April 2002, Pages 53-62
Grant Soremekun, Zafer Gürdal, Christos Kassapoglou, Darryl Toni

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13

 

A genetic algorithm with memory for mixed discrete–continuous design optimization Original Research Article
Computers & Structures, Volume 81, Issue 20, August 2003, Pages 2003-2009
Vladimir B. Gantovnik, Christine M. Anderson-Cook, Zafer Gürdal, Layne T. Watson

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14

 

Elastoplastic truss design using a displacement based optimization Original Research Article
Computer Methods in Applied Mechanics and Engineering, Volume 191, Issues 27–28, 26 April 2002, Pages 2907-2924
Wenjiong Gu, Zafer Gürdal, Samy Missoum

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15

 

Is fatigue of cholestasis mediated by altered central serotoninergic neurotransmission?
Journal of Hepatology, Volume 36, Supplement 1, April 2002, Page 29
Turgay Celik, Nuray Aslan, Zafer Goren, Hakan Gurdal, Tuncer Degim, Murat Toruner, Kubilay Cinar, Tayfun Uzbay, Hakan Bozkaya, Cihan Yurdaydin

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Pipeline implementation of cellular automata for structural design on message-passing multiprocessors Original Research Article
Mathematical and Computer Modelling, Volume 43, Issues 9–10, May 2006, Pages 966-975
Shahriar Setoodeh, David B. Adams, Zafer Gürdal, Layne T. Watson

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17

 

Optimal design of composite wing structures with blended laminates Original Research Article
Composites Part B: Engineering, Volume 38, Issue 4, June 2007, Pages 469-480
Omprakash Seresta, Zafer Gürdal, David B. Adams, Layne T. Watson

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Design of variable-stiffness composite layers using cellular automata Original Research Article
Computer Methods in Applied Mechanics and Engineering, Volume 195, Issues 9–12, 1 February 2006, Pages 836-851
Shahriar Setoodeh, Zafer Gürdal, Layne T. Watson

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19

 

Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage Original Research Article
Computers & Structures, Volume 83, Issues 15–16, June 2005, Pages 1320-1329
Mostafa M. Abdalla, Chevva Konda Reddy, Waleed F. Faris, Zafer Gürdal

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On the variational formulation of stress constraints in isogeometric design Original Research Article
Computer Methods in Applied Mechanics and Engineering, Volume 199, Issues 41–44, 1 October 2010, Pages 2687-2696
Attila P. Nagy, Mostafa M. Abdalla, Zafer Gürdal

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Isogeometric sizing and shape optimisation of beam structures Original Research Article
Computer Methods in Applied Mechanics and Engineering, Volume 199, Issues 17–20, 1 March 2010, Pages 1216-1230
Attila P. Nagy, Mostafa M. Abdalla, Zafer Gürdal

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22

 

Spectral
formulation of finite element methods using Daubechies
compactly-supported wavelets for elastic wave propagation simulation
Original Research Article
Wave Motion, Volume 50, Issue 3, April 2013, Pages 558-578
Lotfollah Pahlavan, Christos Kassapoglou, Zafer Gürdal

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Highlights►
A novel approach that combines a wavelet-based spectral analysis with
FEM is formulated. ► The approach offers possibility of parallel
implementation. ► To achieve hp-refinement capability, the spectral
element method was adopted for spatial discretization.

23

 

Postbuckling response of laminated plates under uniaxial compression Original Research Article
International Journal of Non-Linear Mechanics, Volume 28, Issue 1, January 1993, Pages 95-115
Dong Ku Shin, O.Hayden Griffin Jr, Zafer Gürdal

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Design of stiffened composite panels with a fracture constraint Original Research Article
Computers & Structures, Volume 20, Issues 1–3, 1985, Pages 457-465
Zafer Gürdal, Raphael T. Haftka

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Crimean-Congo haemorrhagic fever presenting as epididymo-orchitis
Journal of Clinical Virology, Volume 48, Issue 4, August 2010, Pages 282-284
Hamit Zafer Aksoy, Gurdal Yilmaz, Firdevs Aksoy, Iftihar Koksal

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Active Aerothermoelastic Control of Hypersonic Double-wedge Lifting Surface Original Research Article
Chinese Journal of Aeronautics, Volume 21, Issue 1, February 2008, Pages 8-18
Laith K Abbas, Chen Qian, Piergiovanni Marzocca, Gürdal Zafer, Abdalla Mostafa

Mike Ciavarella's picture

There is something missing here.

Gurdal is promoter of this thesis in fatigue by Kassapoglou, which is in my understanding very weak and probably suspect in the choice of data that marvellously match the extremely simple theory, but yet Gurdal has not background in fatigue, given he has some papers (and not that many either) in optimization, including quite a lot of them on a very specific topic of "steered fibers" or "variable stiffness design", which is very remote from practical application, but also from fatigue.

What about the other members of Panel commettee in Kassapoglous's thesis that met in 2012?

 

Mike Ciavarella's picture

Curiously, Paul Lagace was Kassapoglou's Master thesis advisor 29 years ago, according to Kassapoglou's phd thesis acknoledgements

 

Acknowledgements
Now that I have come full circle and completed a PhD thesis 34 years after I
started my Bachelor's I look back and realize that I would never have gotten
here if it weren't for some far-sighted and, thankfully, stubborn people who
helped me all along. What follows is not necessarily in order of importance.
First and foremost, Paul Lagace who started as my Master's thesis advisor
29 years ago (I nished both MS degrees 28 years ago by the way) and now
graciously accepted to be a member of my PhD thesis committee. Throughout
the years and, in particular, the past few years when this work started taking
shape, his insightful comments and suggestions were invaluable not the least
of which was that baseball can be exciting especially when the Red Sox win
the World Series. I am indebted to him for not giving up on me.

 

So the supervision was 28 years long and mainly on baseball?  I do not get it!  THis perhaps explains the strange aspect of this phd... 28 years ago, in 2012, this is 1984, so this is when Paul Lagace' had just started at MIT...

 

 

 

Paul
A. Lagacé

Margaret
MacVicar Faculty Fellow
Professor of Aeronautics
and Astronautics
and Engineering
Systems

Dr.
Lagacé received his Ph.D. from
MIT. Upon joining the faculty in 1982,
he concentrated his work in the areas
of mechanics, fracture, longevity,
damage resistance, and damage tolerance
of composite materials and their structures.
He has published widely on these topics
and on general topics related to composite
materials and their structures.

With
this work and his extensive cooperation
with industry as background, he has
been an initiator and key leader of
an effort to improve the methodology
for the design and certification of
composite structures via the recognition
and associated modeling of the various
lengthscales involved in the behavior
of composite structures.

In
later years, he broadened his areas
of engagement to include overall views
of engineering systems, with particular
emphasis on effects of technology.

Dr.
Lagacé has taught courses in
the areas of mechanics of materials
and structures, with special emphasis
on composite materials and their structures,
and has developed courses dealing
with manufacturing with composite
materials and advanced topics in composite
materials and structures. With James
Mar, he developed the video course
series "Composite Materials."
More recently he developed a course
on "Systems Thinking" and
a freshman course on the "Essentials
of Engineering".

Dr.
Lagacé has received departmental
and Institute awards for excellence
in undergraduate teaching, and is
a MacVicar Faculty Fellow. He is a
member of several societies including
being a fellow of the ASTM, a fellow
of the AIAA, a fellow of the ASC,
and an ICCM World Fellow of Composites.
He has served for six years as the
president of the International Committee
on Composite Materials, and has received
various awards. He also serves as
a consultant to industry and as a
participant on various governmental
committees.

Related News:

Paul Lagace profiled in The Boston Globe: “Professor applies wisdom on and off ballfields” – The Boston Globe – November 6, 2011

Paul Lagace Elected AIAA Fellow – November 1999

 

Paul A. Lagacé

Contact
info:

Paul
A. Lagacé

MIT
77 Massachusetts Ave.
Room 33-310
Cambridge, MA 02139-4307

Phone:
617.253.3628
Fax: 617.253.0361
Email to: pal
"at" mit.edu

 

Nothing wrong with that.


What about Reifsneider?

 

 

Mike Ciavarella's picture

Kenneth Reifsnider
Educational Foundation University Professor
Director, Solid Oxide Fuel Cell Center

Kenneth Reifsnider
E-mail:
reifsnid@cec.sc.edu

Phone:
803.777.0084

Fax:
803.777.0106

Office:

541 Main Street

Horizon I Building, Room 334

Columbia, SC 29208

Links:

Solid Oxide Fuel Cell Center

HeteroFoaM Center

Dr. Reifsnider's research and interests include durability,
damage tolerance and strength-life relationships in material systems;
performance of life prognosis, aging, material state changes, long term
behavior; fuel cell science and engineering.

Mike Ciavarella's picture

 

 

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25/ott/2012 - The next big thing in aerospace may just originate from USC – at least if Zafer Gürdal has anything to do with it. Gürdal is an engineer with a ...

 

 

Is all this coincidence???

Mike Ciavarella's picture

 

Furthermore, I am grateful to Zafer Gurdal for insisting that I do this and
helping me all along. I still can't gure out how he manages to combine superb
engineering and academic rigor with intuition that is almost never wrong. I
have learned a lot and look forward to more lessons.

 

Wow, this Zafer Gurdal is respected to be like a God!  With academic rigor and intuition having a combine superb --- leading to disastrous results however!!! :)

 

The remaining committee members, Michel van Tooren, Michael Wisnom,
Kenneth Reifsnider, and Rinze Benedictus are the best members one could
hope for. I am convinced the quality of this thesis would suer a lot if it
weren't for their excellent, and sometimes tough, comments. I am honored.

 

 I guess not sometimes tough, but rather seldom tough comments. If comments were really made, perhaps in view of the age and experience of the candidate 30 years older than standard phd candidate.....

Mike Ciavarella's picture

I read on Gurdal CV that

 

 Research funding from various companies include Sikorsky Aircraft, Ford Motor Co., 

 

So Sikorsky seems to be first in his list at https://www2.aus.edu/conferences/iccst7/documents/prof_zafer_bio.pdf

 

Kassapoglou was working at Sikorsky... I wonder if this is not a conflicct of interest.  Supervising a phd thesis years later having been funded by you.

It is close to being "paid" for later giving loose advice.  And this may well be the case, since Gurdal has no background in fatigue.   I start to see some story....

Mike Ciavarella's picture

Impact Factor:0.936 | Ranking:9/24 in Materials Science, Composites

Source:2012 Journal Citation Reports® (Thomson Reuters, 2013)


Current Issue Cover

  1. Submit an article to this journal

Journal of Composite Materials

 

Editor-in-Chief: Prof H.Thomas Hahn, UCLA, USA

 

The Journal of Composite Materials is
the leading journal of advanced composite materials technology and is
now published 26 times a year. Major areas covered
include: CAD/CAM, Ceramic-matrix composites,
Coatings, Damage mechanics, Design of materials and components,
Environmental
effects, Metal-matrix composites, Modeling,
Non-destructive evaluation, Polymer-matrix composites, Processing and
manufacturing,
Properties and performance, Prototyping
reinforcement materials, Repair, Testing, Thermoplastic
composites,Nanotechnology

Mike Ciavarella's picture

K tends to be underconservative because the SN slope most of the times (say about 8 out of 10) is too shallow.  The SN curve is too "horizontal".  An easy "modification" that in fact was proposed to me by a 3rd year undergraduate (Antonios Catonis) (just to say how easy it is to beat K's theory), is to change the theory so that, if alfa is Weibull 2par shape parameter of static strength, then SN slope may well be

 c alfa instead of alfa, where c is "Catonis corrective factor".

Catonis is now estimating his constant by looking at Navy and FAA databases. 

From the Kassapoglou's model, in a sligthly rielaborated form to obtained close form results, we easily obtain the estimate

    FR(α)=10^{(-6/alfa)}
where FR is fatigue ratio.

In the "Catonis"-corrected form

    FR(α)=10^{(-6/(c alfa) )}

Given the distribution of alfa parameters from Navy or FAA (the scatter of scatter, so we call the alfa parametr, the alfa-alfa, and beta parameter the beta-alfa) which list trovano alfa_alfa= 2 -- 5, e β_alfa=40-50, and given the non-linear transformation above , we obtain in the original K theory tht most specimen would have FR higher than 0.5, which is in sharp contrast with evidence, from the Fleck and Asnhy paper.

But by correcting with Catonis factor, we can change the distribution of FR, because we free up the slope SN from the alfa of scatter, empirically. 

I do not want to disclose all the treatment, as otherwise my student Catonis may be upset not to be able to publish is good improvement of Kassap theory before his 3 years engineering graduation, but with the mathematica command

Plot[Evaluate@
  Table[CDF[
    WeibullDistribution[2.35 , beta], -6/(c Log[10, y])], {beta, {40,
     50}}], {y, 0, 1}, Filling -> Axis, PlotRange -> All]

 you find a reasonably looking distribution of FR, for c=0.3, meaning that the slope of SN curve should be tripled to be realistic!

My compliments to Antonios Catonis, especially as he is a student that does minimum efforts, and is always very active in the class, and making noise and jokes.  Many professors would not like him.  I do :)

Mike Ciavarella's picture

 

Mike Ciavarella's picture

dear FRIENDS

 

I am making progress here, but really I would like this post to involve more people....  please let me know what do you think?   Another ways to improve the theory?

 

 The original abstract from Kassapoglou's first paper, clearly states what he claims

 

ABSTRACT: An approach to construct the stress (or load) vs. cycles curve for
composite structures under constant amplitude loading is presented. The approach is
based on the assumption that the cycles to failure are a function of the probability of
failure during any given cycle. In this first investigation, this probability of failure
during any cycle is assumed to be constant and equal to the probability of failure
obtained from static test results and the associated statistically quantified scatter.
Expressions for the cycles to failure as a function of R ratio are derived. These
expressions do not require any curve fitting and do not involve any experimentally
determined parameters.
The fatigue predictions do not require any fatigue tests for
calibration
. Comparisons to several test cases found in the literature show this first
simple model to be very promising.

 

 

WOW!!!   This is a real strong abstract!  If I ever write an abstract like that in my life, I will be disappointing reviewers like hell!!

 

 Regards

Mike

Mike Ciavarella's picture

I have a feeling that the whole of this story involves some common line of story, it is just that so far I don't get the full picture...  As otherwise people don't expose themselves to such risk of loosing reputations... without a reason!

Mike Ciavarella's picture

Notice the striking difference between what he write in the 2007 paper (and also in the 2012 phd thesis), and what circulates today after my blog in imechanica (2013).



Kassapoglou 1 (2012)

The original abstract from Kassapoglou's first paper, clearly states what he claims

 

ABSTRACT: An approach to construct the stress (or load) vs. cycles curve for
composite structures under constant amplitude loading is presented. The approach is
based on the assumption that the cycles to failure are a function of the probability of
failure during any given cycle. In this first investigation, this probability of failure
during any cycle is assumed to be constant and equal to the probability of failure
obtained from static test results and the associated statistically quantified scatter.
Expressions for the cycles to failure as a function of R ratio are derived. These
expressions do not require any curve fitting and do not involve any experimentally
determined parameters.
The fatigue predictions do not require any fatigue tests for
calibration
. Comparisons to several test cases found in the literature show this first
simple model to be very promising.

 

 

Kassapoglou 2 (2013)



 


He is referencing the wrong paper (2007). And he obviously did not
read my complete thesis even though he references it because the
misunderstanding (I call it misunderstanding to give him the benefit of
the doubt) is clearly explained in the next to last chapter in my
thesis: I never claimed that the cycle by cycle probability of failure
is constant. I claimed that IF it were constant, then elegant solutions
are obtained which I emphasized in the 2007 paper that are of limited
applicability. In the second paper he mentions in 2011 in J Composite
Materials I suggested that the arbitrary assumption of constant
cycle-by-cycle probability of failure follows from a simple differential
equation which still is of limited applicability and is not based on
actual small scale physics but is a qualitative evaluation of residual
strength. He thinks that I consider this as proof.

The sad fact is that he completely missed (or elected to miss) my other 2011 paper:

Kassapoglou, C., and Kaminski, M. “Modeling Damage and Load
Redistribution in Composites Under Tension-Tension Fatigue Loading”,
Composites Part A, 42, 2011, pp. 1783-1792.

In this paper I generalized to the realistic case where the cycle-by-cycle
probability of failure p changes every cycle. This is calculated by
doing exactly what he claims I did not do: Determining different types
of damage at the fiber scale and tracking how it evolves with cycles.
For a series of cross-ply laminates I calculated the value of p as a
function of cycles and which changed drastically and determined the S-N
curve of these laminates with excellent agreement for two laminates and
not so good agreement for the others for reasons explained in the paper.
Which reasons happen to be one of my current research topics with one
of my MS students. Ironically, this paper is based on the last chapters
in my thesis which he seems to have missed.

To make
a long story short: I never claimed the static strength can define the
fatigue life. I only claimed that in the limit, of constant
cycle-by-cycle probability of failure, the resulting equations depend
only on static properties. And hasted to add that this is not
satisfactory for real fatigue behavior and published the above-mentioned
paper from 2011 in Composites Part A generalizing the method.

 

 

I would like to repeat this sentence:

 

In this
paper I generalized to the realistic case where the cycle-by-cycle
probability of failure p changes every cycle. This is calculated by
doing exactly what he claims I did not do: Determining different types
of damage at the fiber scale and tracking how it evolves with cycles.
For a series of cross-ply laminates I calculated the value of p as a
function of cycles and which changed drastically and determined the S-N
curve of these laminates with excellent agreement for two laminates and
not so good agreement
for the others for reasons explained in the paper.

 


To make
a long story short: I never claimed the static strength can define the
fatigue life. I only claimed that in the limit, of constant
cycle-by-cycle probability of failure, the resulting equations depend
only on static properties. And hasted to add that this is not
satisfactory for real fatigue behavior and published the above-mentioned
paper from 2011 in Composites Part A generalizing the method.

 


Dr. KASSAPOGLOU, apart from discussing the way you mistreat poor statistical theory in many respects, THE PROBLEM IS ANOTHER.  YOU CANNOT CALCULATE FATIGUE!!!  You keep thinking you can do that, in all the papers!   YOU NEED FITTING CONSTANTS, OR EMPIRICAL EQUATIONS; BUT FITTED TO DATA OF SN CURVES, NOT CALCULATED.  IF YOU KEEP CALCULATING, IT MEANS YOU ARE USING AS ONLY DATA THE STATIC ONES!   DO YOU REALIZE THIS?



 

 

The funny tentative to confuse the reader doesn't go very far.  Obviously a detailed statistical analysis of the errors conducted in the many versions of the wrong model requires separate papers, which I will send to the Editor of JCM first, and other journals later.

But the paradox is that he still hasn't learned the lesson:  he still claims that by making the cycle-by-cycle probability change depending on mechanism, he can "predict" fatigue!   There is risk that large sums of research funding will be spent to follow this confused and confusing program.  It would be good to have a chance to talk to Kassapoglou directly to explain him the problems and collaborate on his model. But missing this opportunity, I will write a few papers as soon as I found the time.  My 2nd year undergraduate student Antonios Catonis is anyway already following a more promising path, by empirically fitting with "pseudo" Kassapoglou SN curves, 3 independent large databases.  This will be a matter of few equations in Mathematica, and cannot claim millions of research money, but isn't this what the scientific world should do?  Simplify things and make them easier and cheaper, rather than confuse and ask more research money?  I am lost. 

Mike Ciavarella's picture

dear Prof. Harris

  I don't know if you are aware of the Kassapoglou strange theory on composite fatigue, based originally on a 2007 paper, and later developed into 2 more.  All 3 attached.

The 2007 paper strangely refers only to your data in a 1994 paper which I haven't been able to download (can you please give me a copy)?

Gathercole, N., Reiter, H., Adam, T. and Harris, B. (1994). Life Prediction for

Fatigue of T800/5245 Carbon-fibre Composites: I. Constant Amplitude Loading. Fatigue, 16: 523–532.

There was some "scandal" over K's theory recently, you may read here.

http://imechanica.org/node/14994

I find it strange that, for such huge claims he made, he only referred to your paper ---- either it was the only datat that matched his theory (later, 3 independent groups found the theory completely invalid), or else he is not even reporting your data correctly.   Which one you can tell?

I look forward to discuss more about this fatigue theory, I have developed quite a number of alternative or competitive solutions.

-- 

Best regards

Prof. Michele Ciavarella. Politecnico di BARI, Rector's delegate to National Research Council

 

Mike Ciavarella's picture

I have been told that Prof. Harris has retired.

The data may well be correctly taken by Kassapoglou, as well as a reference in the text where he may have taken ispiration to develop his model.

In fact, at pag.527 it is written, talking of the Weibull shape parameter for lives (what we call more often alfa_L)

 It is interesting to note that for an rn
value of unity, which is very nearly the case for these
pooled data, the Weibull model reduces to a simple
exponential distribution. The exponential distribution
is sometimes used to model distributions of failure
times for the reliability of a product. It is pointed out
by Chatfield [17] that the exponential distribution governs
systems where age has no influence on the probability
of failure. If a component survives for a length of
service t, the probability of failure within a subsequent
time interval from t to (t + At) is hAt, where h is a
constant for all t. Thus failure is a random event, and
the system does not deteriorate as a result of service.
This would not normally be thought applicable to the
fatigue failure of reinforced plastics for which it is
known that residual performance is in fact reduced as
a result of the accumulation of damage.
We note,
however, that the value of the shape parameter derived
from this analysis is identical with that obtained by
Whitney, quoting data by Ryder and Walker TM, of
m = 1.1 for a similar type of carbon fibre composite,
a remarkable degree of correspondence.

 So, I guess Kassapoglou was induced to look at these Chatfield book "Statistics for technology" Penguin, Harmondswort, 1970.  Now we can see where the process comes from, as I suspected. It comes from reliability theory for systems with no degradation. However, those authors were wise to say

This would not normally be thought applicable to the
fatigue failure of reinforced plastics for which it is
known that residual performance is in fact reduced as
a result of the accumulation of damage.
 

although when they said We note,
however, that the value of the shape parameter derived
from this analysis is identical with that obtained by
Whitney, quoting data by Ryder and Walker TM, of
m = 1.1 for a similar type of carbon fibre composite,
a remarkable degree of correspondence.

then they attracted the interest of Kassapoglou, who was looking for instant fame to find out how come, despite wear-out, the results appear (at least in terms of scatter of fatigue life) still very close....

Dear Prof. Ciavarella,

I am a graduate student and do not claim any specific expertise in the discussed matter, for I will leave the scientific discussion to the specialists.

I would just like to ask, as the most humble of students, if a blog is the correct place at all for a scientific debate: maybe it is apt for surreptitiously suggesting scandals, conspiracy theories involving funding, PhD awarding panels, etc., but I very much doubt  is better than a Journal to truly aim at establishing whatever could be meant by "scientific truth".

If the theory under discussion is so flawed there will not be any difficulties for your worst student, let alone yourself, to expose why it is so in a publication ,which I am sure will be read with extreme interest by Dr. Kassapoglou himself.

Otherwise science might be better left aside, the joys of literature are not be undervalued at all:

" Il sangue mio d'invidia sì riarso
che se veduto avesse uomo farsi lieto,
visto m'avresti di livore sparso"

a (poor) free translation of these verses from Dante's Purgatory being

 "My blood was so consumed by envy

you would have seen me covered in lividness,

if I saw a man making himself happy"

 

Best Regards

Marco

Mike Ciavarella's picture

Of course I will write to the Editors.  But there are situations sometimes that are so big that writing to an Editor, you simply get rejected. Or if not, you are accepted, but people continue to say that you have just a different model.


I am glad you never experienced the very harsch environments.  I had to refuse a good offer from MIT to work in Russia,  because even MIT was unable at that point to stop some people going along, despite I made evident what was going on.

No, there are situations where a letter to an Editor doesn't solve anything....  and maybe not even Imechanica blog.  Situations are very complex, if they involve a russian center which was decided by Medvedev, then MIT was contracted to organize it, then Putin came back to power, then Medvedev declared he would run for President in 2018, then Skoltech and Skolkovo became unfriendly places for Putin.  At the same time, in Russia, building a center with billions of dollars raises the interest of big players, and these people, I can promise you, care very little of a letter to an editor.

My own refusal to be head of mech of mat of ASPEM, in good terms

So, I am just limiting myself to the scientific discussion, which will continue in journals, but the blog permits to speak more openly and suggest other hidden versions of the history of some (bad) parts of out community.

 

PS: since you like Dante, why do you think his guide to the truth (Virgilio) is blind?

 

PS2:  I am in good terms with MIT, and hope to collaborate with them.  They are doing their best, and I think I can help them in the future, to improve the situation.

Prof. Ciavarella,

I am not familiar with the geopolitical background of the Skolkovo project.

While I do not have any difficulty in believing what you say, I wonder what the relevance to the actual discussion is.

You evidently firmly hold the view, and display it proudly, that in a blog such as Imechanica is correct to " suggest other hidden versions of the history of some (bad) parts of out community": I personally find it astonishing that a Professor, in my (possibly old-fashioned) view of society a member of the highest elite, could even consider talking about hidden versions of history without the presence of the defendant.

Incidentally, I could not help noticing you very often refer to hidden histories: this is a highly curious attitude for an individual who I am certain without any doubts  never ever got close to events such as fake examinations, geared exam commissions, "sponsored" promotions, politically driven funding, etc. etc.

Please also note that Virgilio was not blind.

Homer was reportedly blind, as well as the classical representation of Justice.

Popular wisdom argues blindness is useful (necessary?) to the Judge and the Poet in order to be able to look at the essence of the World, not the festering accidents (in the classical sense of the word) disguising it.

Kind Regards

 Marco

Mike Ciavarella's picture

 

Don't worry about the defendant, in case you want to be his lawyer.  He knows very well this debate, never wanted to enter it in person, in public, and now in blogs.  It is his right and his choice.  The only way he likes to do it, is behind the curtains. 

By the way, your english is very good indeed.  As a lawyer, you should declare your name, and I start to think you are not italian!    Perhaps you are not too far from the defendant himself?   Then lets talk science, and stop this going round circles.... :)

Prof. Ciavarella,

 I do not worry about the defendant, with whom I never had the pleasure to interact. I worry about the principle.

It infuriates me to see a fellow Italian giving a chance for the worst stereotypes on our Country to find immediate use.

On the other hand, I perfectly appreciate it was none of my business: I acted impulsively and regret having interrupted the debate.

In parallel, I now fear my post-doc application for Politecnico di Bari is endangered...

I wish I could accept your final invitation, but as I have prefaced I do not know much about the topic, certainly not enough to engage in a discussion with you. I am reading the various papers for my own benefit though, I suppose I should be grateful for having stimulated my interest.

Regards

 Marco

 

 

Mike Ciavarella's picture

Too bad there is no post-doc position in Bari open.   Good attempt!   Everybody knows by now what kind of tricks you play.  I will be glad to return to scientific discussion, where of course you don't like people to recognize the tricks.

Prof. Ciavarella,

sarcasm seems not be in your chords, if you only considered my statement on Bari's Politecnico as possibly sincere ( I must have really cared a lot about that application to get into today;s conversation with you hey? James Bond would not have been subtler...) and not for what it was (the very colorfoul expression the locals use up here to describe such linguistic jokes could possibly offend some fellow bloggers, and I will not mention it: sufficient to say it refers to a very natural, yet private, human act).

How can anybody, let alone an intellectual, only think that somebody else would disguise themselves as a student, open an ID on a blog, post a couple of months before a couple of unrelated questions (evidently, to perfection his cover-up), lie on their nationality!, just to spend the day chit chatting on a blog, is truly out of my understanding: but I am glad you found new material for your plot theory.

Regards

Marco

Mike Ciavarella's picture

Not hide under an italian name nobody can verify.   This is the difference, I put my name on my "scientific stories".  Here, we have a scientific debate, the defendant doesn't want to appear.  Now, another guy with a random name appears, and he wants to convince the audience that I am the paranoid guy?  Quite difficult.

In any case, I have raised scientific concerns, and will respond only to scientific questions from now on.  I will see if you continue to have strength on those fields.

My name is Marco Musto: as you can see from my surname, as Italian as one could be!

I apologise for not having it declared immediately, I was adamant the surname was available for everybody to check on my Imechanica account informations, I would have never had this discussion in an anonymous fashion.

Should you imply my name is fake as well, I will unfortunately consider the limit of offence reached.

As further verification, we could go back to our mother tongues, unless you suggested I have an italian friend sitting next to me: I do really hope there will be no need for such exercises. I am mortified by the fact anybody could think I were Dr. Kassapoglou, regardelss of his scientific work I could not stand causing any harm to his reputation.

For your scientific concerns and questions, I am sure the  community will be of much more use than me, as I declared at the beginning and on another couple of occasions my ignorance on the matter.

I am on the other hand relieved that you consider the conversation over.

Best Regards

Marco

Mike Ciavarella's picture

This is fine.  One more thing you forget.  At one point you declared you were my post-doc candidate, to imply I am not offering this position.  Where this story came from?  Now that your name is material, and since there is no post-doc position in Bari open that I know of, can you explain please?

Prof. Ciavarella,

 as you ask so gracioulsy, I hereby confirm, Urbi et Orbi,  I am not your post-doc candidate, I was not implying you are not offering such position nor the opposite, and in general by no means I was trying to imply / suggest / drive the reader to think anything bad or disreputable with regards to Prof. Ciavarella and the Instituion he represents. The post-doc line was a joke.

What I said and think and I am entirely responsible for is written in black ink.

Regards

 Marco

 

Mike Ciavarella's picture

I like that you were making humour, and I don't lack of such sense.  Actually I suspect you come from Napoli, where there is abundance of such.

 So should you look at the scientific content, you will also find it interesting.  It is easy to understand Kassapoglou's wrong, less obvious to dissolve all the tricks that are nested one into the other...  plus the data manipulation which must have occurred.

Good luck with your studies, I am sure you'll do good, and in case you're looking for post doc one day, who knows I have the possibility to offer it to you :)

 Mike

All the best for your career and projects too, I will certainly read the papers and follow this discussion.

Best Regards

Marco

 

Mike Ciavarella's picture

I had a nice conversation with a famous professor, who is old fashioned and does not wanto to appear.  I will mix his messages to mine, and

hence we don't really quote him, either wrong or right.

 

 

Using FAA data of a 2011 report, I found a correction of Kassapoglou's theory, which admits from the outset that
it is completely empirical, and has only ONE fitting constant INSTEAD OF NONE in Kassapoglou, and TWO in most theories. 
Also, the advantage is that this SINGLE fitting constant one can derive approximately estimating huge databases.

In other words, I assume power law SN curve, and adapt the slope NOT to be fixed as in the original (wrong)
Kassapoglou's theory. Assuming the constant from the largest databases around (Navy, and Fleck - Ashby), the
single constant is about 0.3 and improves the error of Kassapoglou a lot, particularly as it becomes a conservative method.

Many good people are not interested in such empirical fits.  This is why perhaps Kassapoglou has escaped attention.
Not only he is trying an empirical fit, he is actually trying an analytical one!  So people do not beleive it even possible
and do not even read it.

Many people do not see any point in pointing out the
deficiencies in such an approach, but prefer to offer a more positive alternative approach which explicitly
includes the mechanisms of fatigue damage propagation and then failure.  They do not think that the empirical
approaches will ever contribute much to our ability to predict fatigue life of engineering components, and
also believe that they have the potential to provide non-conservative predictions, particularly when there
are slight changes to the loading and/or the effects of manufacturing defects are not accounted for. 

They have not paid close attention to progress in this field as a result.

Mike Asbhy has always searched first for first rules of thumb and simple equations, then very full and rich diagrams
including many data, and then perhaps more refined models. 

We should ask Mike Ahsby to give a third opinion then!

Seriously, the modelling of fatigue in composites with detailed models I think is an area which may lead to a respectable career,
but not to serious advancements.   If ultimately I want to know how to certify and design a plane, I cannot use detailed models,
which in any case will require detailed experiments, and detailed certification.

So I guess we have a lot of interesting discussions to make :)  

How many people would give attention then now to my simplified empirical approach (which takes the wrong Kassapoglou approach
and put it back to work more or less, but empirically with fitting constants?). It may be taken even worse than the original
Kassapoglou?  Or at least the people who were skeptical of Kassapoglou's claim will be happy?

Or the people who did not like the idea itself, will take my improvement and the original Kassapoglou's work as not interesting?

Mike Ashby has a nice phrase:  "model-informed empiricism",  this underlies his deformation mechanism maps. 
I.e. Diffusional creep or power law creep etc have a simple empirical equation which defines them, but that
there is also an underlying model, with physically significant parameters (e.g. For dislocation glide and climb)
with e.g rate constants and activation energies that can be independently measured from the creep/plastic
deformation that they describe.  I completely understand and endorse this. 

But for some poeple what is missing in purely empirical models for composite fatigue is generally any acknowledgement
that the underpinning mechanisms matter. 

One of Mike Asbhy's key warnings is regarding the danger of extrapolating across mechanism boundaries.

One simple example from the testing of composite coupons:  In tension-compression fatigue of a composite laminate,
the initial damage mechanisms are typically a combination of off-axis ply cracking and then delamination. 
Delamination growth can be quite well-described by a "Paris Law" (which is empirical, but based on the model
of fracture mechanics).   Failure typically occurs when some of the delaminations have extended across the coupon
width and created sublaminates that fail in buckling on the compression part of the cycle, sublaminate-buckling
is also quite amenable to modeling.  An empirical model that is going to fit the life of such a coupon needs to
say something about both the load dependence of delamination growth and buckling failure and also the effect of
lengthscales, including the ply and laminate thickness (which control edge delamination growth) specimen width
(which controls the number of cycles required to allow a delaminated sub-laminate to extend across the specimen width),
and the lengthscales involved in sublaminate buckling.  Even when a model has captured all of these physical elements,
there is no guarantee that the same mechanisms will apply in a larger structure.  For instance aircraft structures
have very few free edges from which delaminations can initiate.  I could add a number of other geometries and
loading cases for which I have a basic understanding of the underlying mechanisms, e.g. Open holes, ply drops,
adhesive joints, effects of voids and face-sheet seams.

I restart from this point: Mike Ashby has a nice phrase: 

"model-informed empiricism",  this underlies his deformation mechanism maps. 

I know to some extent the approach of Ahsby for wear-mechanisms, for failure-mechanisms,
but let's look at the case of fatigue. The paper is Fleck and Ahsby 1994.

ESTIMATE FOR FATIGUE LIMIT
The endurance or fatigue limit oe is the stress
amplitude which a smooth, unnotched sample will
sustain without fracture for 10 7 cycles; for many
practical purposes 10^7 cycles can be thought of as
"infinite" life. Most data derive from tests (such as
the rotating-bend test) in which the mean stress is
zero and R = - 1; for this reason the endurance limit
is usually quoted for R =-1. We follow this
convention in presenting values for the endurance
limit later in the paper.

Given the need for slip, it is not surprising that the
endurance limit, for a given class of materials, is
proportional to the yield strength (Section 4.1,
below). The full microscopic model for the shape of
the S-N curve is more difficult, for the reason given
earlier. It is the failure envelope associated with a
sequence of interdependent phenomena: cyclic
hardening, crack nucleation and cyclic growth, and
final fast fracture.

So no real equations!  Only testing can do good estimates.
There are of course engineering equations, mostly based
on hardness.  I am not sure why Fleck et Asbhy do not mention
them.  These in turn can be put also in terms of ultimate
strength, and hence we can derive the fatigue ratio.

ESTIMATE FOR DK-THRESHOLD
There are some estimates based on elastic modulus.
But despite the consistency of these estimates, the
models, while perhaps realistic for fatigue under
vacuum with no anelastic heating, are incomplete;
they do not, for instance, explain the established
dependence of AKth on the environment in which the
test is carried out.

ESTIMATE FOR PARIS LAW CONSTANTS

In its simplest dimensionally consistent--though not very accurate---form
this becomes (10), where C is found empirically (4) to have a value of
approximately 3.
There is some more discussion about the relation between Paris' law constants.

In conclusion, we don't have even in Fatigue real models for the various mechanisms (except the phenomenological
SN Wohler Basquin Coffin Manson one, and Paris), why should we hope any easier the situation for composites??

In conclusion, I think the key point at present is to have in composite materials
what we have for metals design.  Some rules of thumb.  Kassapoglou has the merit
to have raised this issue, but has the demerit to have solved it in a wrong
manner.  But things can be improved.  There are various correct models based
on measuring wearout, and these need some experimentally validated fitting constants
and it is possible also to say something general, like I am trying to do, and Ashby perhaps
would like.

The change of mechanisms is extremely important of course, but how to deal with that?
Ashby usually does it by fitting a model to a mechanism, and another to another mechanism.

But if there is no real model for composite fatigue other than fitting models, the Ashby worry about
transitions and extrapolation between mechanisms reduces to a worry about regions of validity of
fitting models, and regions of validity of fitting constants.

But there is nothing very new there. 

Mike Ciavarella's picture

The paper is also soon to appear in ArXiv, so you will see the full content, and comment.

 

Here are abstract and conclusions.

 

A critical assessment on Kassapoglou’s

statistical model for composites fatigue

M. Ciavarella

Politecnico di BARI, V.le Gentile 182, 70125 Bari, Italy

Corresponding author: mciava@poliba.it

V. Vinogradov

School of Civil Engineering & Geosciences,

Newcastle University, Newcastle upon Tyne, NE1 7RU, U.K.

G. Carbone

Politecnico di BARI, V.le Gentile 182, 70125 Bari, Italy

Abstract

Kassapoglou recently proposed a model for fatigue of composite

materials which seems to suggest that fatigue SN curve can be entirely predicted on the basis of the statistical distribution of static

strengths. The original abstract writes “Expressions for the cycles to

failure as a function of R ratio are derived. These expressions do not

require any curve fitting and do not involve any experimentally determined parameters. The fatigue predictions do not require any fatigue

tests for calibration”. These surprisingly ambitious claims and attractive results deserve careful scrutiny. We contend that the results seem

to be due to a number of approximations and incorrect derivations,

and one particular misleading assumption, which make the model not

conform to a fatigue testing in a given specimen with resulting SN 

curve distribution. The quantitative agreement of some predictions

(the scatter of distribution of fatigue lives being close to the mode

value found in typical composites of aeronautical interest in the large

Navy database) should not motivate any enthusiasm. It is believed

that a proper statistical treatment of the fatigue process should not 

make wear-out constants disappear, and hence the SN curves would

depend on them, and not just on scatter of static data. These serious concerns explain the large discrepancies found by 3 independent

studies which tried to apply Kassapoglou’s model to composite fatigue

data, and to other well known results. 

 

6 Conclusion

In the original K’s model there is a confusion between what we call fatigue

and statistics of the static strength of a number of specimens. Fatigue life

(number of cycles) is mistakenly replaced with the number of tested specimens to find a specimen with strength less than applied load. This number

of specimen indeed solely depends on the initial statistical distribution of the

static strength, while fatigue is related to damage accumulation in a specimen and its strength degradation with cycles, which contradicts the main

assumption. One can also mistakenly deduce from the proposed model that

if there is no dispersion in the static strength, for instance, all the specimen

have exactly the same static strength, there is no such thing as an SN curve.

K model is an interesting attempt of using wear-out models with degradation deterministic equations to predicting SN curves from static data only

for composites (something which is not easy even with metals). However,

its results don’t look realistic at all, and indeed we have explained here why.

Not surprisingly, SN curves found in many independent assessments were

found to be (generally) unconservative for the vast majority of data (10 sets)

considered in FAA 2011 report [15], at least by 1-2 orders of magnitude.

We have given reasons for this effect, both theoretically and with additional

estimates from large set of results from databases of composite materials.

Only ”fitting” models can be considered reliable, as discussed by Vassilopoulos & Keller [16], and it should be remarked in this respect that an 

6 Conclusion

In the original K’s model there is a confusion between what we call fatigue

and statistics of the static strength of a number of specimens. Fatigue life

(number of cycles) is mistakenly replaced with the number of tested specimens to find a specimen with strength less than applied load. This number

of specimen indeed solely depends on the initial statistical distribution of the

static strength, while fatigue is related to damage accumulation in a specimen and its strength degradation with cycles, which contradicts the main

assumption. One can also mistakenly deduce from the proposed model that

if there is no dispersion in the static strength, for instance, all the specimen

have exactly the same static strength, there is no such thing as an SN curve.

K model is an interesting attempt of using wear-out models with degradation deterministic equations to predicting SN curves from static data only

for composites (something which is not easy even with metals). However,

its results don’t look realistic at all, and indeed we have explained here why.

Not surprisingly, SN curves found in many independent assessments were

found to be (generally) unconservative for the vast majority of data (10 sets)

considered in FAA 2011 report [15], at least by 1-2 orders of magnitude.

We have given reasons for this effect, both theoretically and with additional

estimates from large set of results from databases of composite materials.

Only ”fitting” models can be considered reliable, as discussed by Vassilopoulos & Keller [16], and it should be remarked in this respect that an additional interesting wearout model is [21-23].

 

References

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Materials 1975; 9: 297-311.

2. Sendeckyj GP. Fitting models to composite materials fatigue data. test methods

and design allowables for fibrous composites, In: Chamis CC (ed) ASTM STP 734.

Philadelphia, PA: American Society for Testing and Materials, 1981, 245-260.

3. Kassapoglou C. Fatigue life prediction of composite structures under constant

amplitude loading. J of Composite Materials 2007; 41: 2737-2754.

4. Kassapoglou C. fatigue model for composites based on the cycle-by-cycle probability of failure: implications and applications, J of Composite Materials 2011;

45: 261-277.

5. Kassapoglou C. 2012. Predicting the structural performance of composite structures under cyclic loading, PhD thesis, Delft Univ of Technology.

http://repository.tudelft.nl/assets/uuid:73a4025d-c519-4e3a-b1cd-c1c8aa0...

full document v3.pdf.

6. Juvinall RC and Marshek KM. Fundamentals of machine component design.

5th ed. John Wiley & Sons Inc, 2011.

7. Lee J-W, Daniel IM and Yaniv G. Fatigue life prediction of cross-ply composite

laminates. In: Lagace PA (ed) Composite Materials: Fatigue and Fracture, Second

Volume. ASTM STP 1012. Philadelphia, PA: American Society for Testing and

Materials, 1989, pp. 19-28.

8. Gathercole N, Reiter H, Adam T and Harris B. Life prediction for fatigue of

T800/5245 carbon-fibre composites: I. Constant amplitude loading. Fatigue 1994;

16: 523-532.

9. Amijima S, Fujii T and Hamaguchi M. Static and fatigue tests of a woven glass

fabric composite under biaxial tension-torsion. Composites 1991; 22: 281-289.

10. Cvitkovich MK, O’Brien TK and Minguet PJ. Fatigue debonding characterization in composite skin/stringer configurations. In: Cucinell RB (ed), ASTM

STP 1330, Philadelphia, PA: American Society for Testing and Materials, 1998,

pp. 97–121.

11. O’Brien TK. Fatigue delamination behavior of peek thermoplastic composite

laminates. J. Reinforced Plastics and Composites 1988; 7: 341-359.

12. O’Brien, TK, Rigamonti M and Zanotti C. Tension fatigue analysis and life

prediction for composite laminates. Hampton, VA: National Aeronautics and Space

Administration. Technical Memorandum 100549, 1988.

13. Maier G, Ott H, Protzner A and Protz B. Damage development in carbon fibrereinforced polyimides in fatigue loading as a function of stress ratio. Composites

1986; 17: 111–120.

14. Gerharz JJ, Rott D and Schuetz D. Schwingfestigkeitsuntersuchungen an Fuegungen in Faserbauweise, BMVg-FBWT, 1979. pp. 79-23.

15. Tomblin J and Seneviratne W. Determining the fatigue life of composite aircraft structures using life and load-enhancement factors. Report DOT/FAA/AR-

10/6. Federal Aviation Administration, National Technical Information Service, 

Volume. ASTM STP 1012. Philadelphia, PA: American Society for Testing and

Materials, 1989, pp. 19-28.

8. Gathercole N, Reiter H, Adam T and Harris B. Life prediction for fatigue of

T800/5245 carbon-fibre composites: I. Constant amplitude loading. Fatigue 1994;

16: 523-532.

9. Amijima S, Fujii T and Hamaguchi M. Static and fatigue tests of a woven glass

fabric composite under biaxial tension-torsion. Composites 1991; 22: 281-289.

10. Cvitkovich MK, O’Brien TK and Minguet PJ. Fatigue debonding characterization in composite skin/stringer configurations. In: Cucinell RB (ed), ASTM

STP 1330, Philadelphia, PA: American Society for Testing and Materials, 1998,

pp. 97–121.

11. O’Brien TK. Fatigue delamination behavior of peek thermoplastic composite

laminates. J. Reinforced Plastics and Composites 1988; 7: 341-359.

12. O’Brien, TK, Rigamonti M and Zanotti C. Tension fatigue analysis and life

prediction for composite laminates. Hampton, VA: National Aeronautics and Space

Administration. Technical Memorandum 100549, 1988.

13. Maier G, Ott H, Protzner A and Protz B. Damage development in carbon fibrereinforced polyimides in fatigue loading as a function of stress ratio. Composites

1986; 17: 111–120.

14. Gerharz JJ, Rott D and Schuetz D. Schwingfestigkeitsuntersuchungen an Fuegungen in Faserbauweise, BMVg-FBWT, 1979. pp. 79-23.

15. Tomblin J and Seneviratne W. Determining the fatigue life of composite aircraft structures using life and load-enhancement factors. Report DOT/FAA/AR-

10/6. Federal Aviation Administration, National Technical Information Service, 

Volume. ASTM STP 1012. Philadelphia, PA: American Society for Testing and

Materials, 1989, pp. 19-28.

8. Gathercole N, Reiter H, Adam T and Harris B. Life prediction for fatigue of

T800/5245 carbon-fibre composites: I. Constant amplitude loading. Fatigue 1994;

16: 523-532.

9. Amijima S, Fujii T and Hamaguchi M. Static and fatigue tests of a woven glass

fabric composite under biaxial tension-torsion. Composites 1991; 22: 281-289.

10. Cvitkovich MK, O’Brien TK and Minguet PJ. Fatigue debonding characterization in composite skin/stringer configurations. In: Cucinell RB (ed), ASTM

STP 1330, Philadelphia, PA: American Society for Testing and Materials, 1998,

pp. 97–121.

11. O’Brien TK. Fatigue delamination behavior of peek thermoplastic composite

laminates. J. Reinforced Plastics and Composites 1988; 7: 341-359.

12. O’Brien, TK, Rigamonti M and Zanotti C. Tension fatigue analysis and life

prediction for composite laminates. Hampton, VA: National Aeronautics and Space

Administration. Technical Memorandum 100549, 1988.

13. Maier G, Ott H, Protzner A and Protz B. Damage development in carbon fibrereinforced polyimides in fatigue loading as a function of stress ratio. Composites

1986; 17: 111–120.

14. Gerharz JJ, Rott D and Schuetz D. Schwingfestigkeitsuntersuchungen an Fuegungen in Faserbauweise, BMVg-FBWT, 1979. pp. 79-23.

15. Tomblin J and Seneviratne W. Determining the fatigue life of composite aircraft structures using life and load-enhancement factors. Report DOT/FAA/AR-

10/6. Federal Aviation Administration, National Technical Information Service, 

 18. Fleck NA, Kang KJ, Ashby MF. Overview no. 112: The cyclic properties of

engineering materials, Acta Metallurgica et Materialia 1994; 42: 365–381

19. Whitehead RS, Kan HP, Cordero R and Saether ES. Certification Testing

Methodology for Composite Structures, Vol I and II. Naval Air Development Centre

Report No. 87042-60 (DOT/FAA/CT-86-39), 1986.

http://www.dtic.mil/dtic/tr/fulltext/u2/b112288.pdf

20. Kassapoglou C and Kaminski M. Modeling damage and load redistribution in

composites under tension-tension fatigue loading, Composites: A 2011; 42: 1783–

1792.

21. D’Amore A, Caprino G, Stupak P, Zhou J and Nicolais L. Effect of stress ratio

on the flexural fatigue behaviour of continuous strand mat reinforced plastics.

Science and Engineering of Composite Materials 1996; 5: 1-8.

22. Caprino G and D’Amore A. Flexural fatigue behaviour of random continuous fibre reinforced thermoplastic composites. Composite Science and Technology

1998; 58: 957-965.

23. D’Amore A, Caprino G, Nicolais L and Marino G. Long-term behaviour of

PEI and PEI-based composites subjected to physical aging. Composites Science

and Technology 1999; 59: 1993-200.

Mike Ciavarella's picture

 

 poliba.it

Your submission submit/0816804 has been assigned the permanent arXiv
identifier 1310.1455 and is available at:

http://arxiv.org/abs/1310.1455

Abstract will appear in today's mailing as:
------------------------------------------------------------------------------
\\
arXiv:1310.1455
From: Michele  Ciavarella <mciava@poliba.it>
Date: Sat, 5 Oct 2013 08:29:05 GMT   (368kb)

Title: A critical assessment on Kassapoglou's statistical model for composites
  fatigue
Authors: M.Ciavarella, V.Vinogradov, G.Carbone
Categories: cond-mat.mtrl-sci
Comments: 3 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
\\
  Kassapoglou recently proposed a model for fatigue of composite materials
which seems to suggest that fatigue SN curve can be entirely predicted on the
basis of the statistical distribution of static strengths. The original
abstract writes "Expressions for the cycles to failure as a function of R ratio
are derived. These expressions do not require any curve fitting and do not
involve any experimentally determined parameters. The fatigue predictions do
not require any fatigue tests for calibration". These surprisingly ambitious
claims and attractive results deserve careful scrutiny. We contend that the
results seem to be due to a number of approximations and incorrect derivations,
and one particular misleading assumption, which make the model not conform to a
fatigue testing in a given specimen with resulting SN curve distribution. The
quantitative agreement of some predictions (the scatter of distribution of
fatigue lives being close to the mode value found in typical composites of
aeronautical interest in the large Navy database) should not motivate any
enthusiasm. It is believed that a proper statistical treatment of the fatigue
process should not make wear-out constants disappear, and hence the SN curves
would depend on them, and not just on scatter of static data. These serious
concerns explain the large discrepancies found by 3 independent studies which
tried to apply Kassapoglou's model to composite fatigue data, and to other well
known results.

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